A theoretical foundation, metrics and modeling of packet reordering and methodology of delay modeling using inter-packet gaps

  • Authors:
  • Anura P. Jayasumana;Nischal Murthy Piratla

  • Affiliations:
  • Colorado State University;Colorado State University

  • Venue:
  • A theoretical foundation, metrics and modeling of packet reordering and methodology of delay modeling using inter-packet gaps
  • Year:
  • 2005

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Abstract

Increased parallelism required to handle high link speeds, large routing tables, wireless ad hoc routing, and enhancement features such as QoS and overlay routing, are some of the factors that point to an increase in reordering on Internet. Unchecked, reordering will have a significant detrimental effect on the end-to-end performance. A formal representation of reordering is presented based on reorder event, reorder set, reorder segment, and basic patterns. "Reorder Density" (RD) metric is defined for measurement and characterization of reordering. Properties of RD are derived. RD maintains the interdependency between the packets using principle of conservation of reordering in a sequence. Reorder response, defined as the RD of a received sequence when packets are sent in-order at the sender, captures reordering introduced by a network. Under stationary operating conditions, it is shown that the reorder response of the network formed by cascading two subnets is equal to the convolution of the reorder responses of individual subnets. The concept of "Reorder Buffer-occupancy Density" (RBD) is defined based on the occupancy of a reorder recovery buffer. RD, RBD and other proposed metrics for reordering are evaluated using a framework developed for comparison and analysis of reorder metrics. The framework consists of attributes that include capturing reordering, low sensitivity to lost and duplicated packets in reorder measurements, usefulness, simplicity, evaluation complexity, etc. Models for packet reordering in terms of RD and RBD are presented for two-path load splitting, limiting reordering to basic pattern formations. For RD, general models of reordering are presented for multi-path load splitting without pattern limitations. All these models are verified using emulated topologies. The end-to-end delay of packets in data streams is characterized with emphasis on effects due to cross traffic, sending rate, and packet size. Measurements indicate that modeling delay of a stream with high sending rates, as a fraction of bandwidth, is difficult due to the correlations among the delay values. The correlations among inter-packet gaps (IPG) at these rates however are negligible. At lower rates, the delay correlations are negligible, and the distribution of delay can be used for delay model. We exploit the relation between delay and IPG to show how a Markov process can be used to approximate end-to-end delay.